Pseudoholomorphic curve

Summary

A pseudoholomorphic curve, or $J$-holomorphic curve, is a map from a Riemann surface into an almost complex manifold whose differential is complex linear. On a symplectic manifold with a compatible almost complex structure, the moduli spaces of such curves carry topological information. Gromov introduced them in 1985, and they are the basis of Gromov–Witten invariants, Floer homology and Fukaya categories.